Simulation of Antiplane Piezoelectricity Problems with Multiple Inclusions by the Meshless Method of Fundamental Solution with the LOOCV Algorithm for Determining Sources

Jingyi Zhang, Ji Lin (), Fajie Wang and Yan Gu ()
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Jingyi Zhang: College of Mechanics and Engineering Science, Hohai University, Nanjing 210098, China
Ji Lin: College of Mechanics and Engineering Science, Hohai University, Nanjing 210098, China
Fajie Wang: College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
Yan Gu: Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China

Mathematics, 2025, vol. 13, issue 6, 1-24

Abstract: This paper provides a high-accuracy and efficient method for addressing antiplane piezoelectricity problems with multiple inclusions. The method of fundamental solutions is a boundary-type meshless method that applies the linear combination of fundamental solutions as approximate solutions with the collocation method for determining the unknowns. To avoid the singularity of fundamental solutions, sources are placed away from the physical boundary. The leave-one-out cross-validation algorithm is employed to identify the optimal source placements to mitigate the influence of this singularity on numerical results. Numerical results of the stress concentration and electric field concentration at the interface between circular and elliptic inclusions and matrix are studied and compared well with references. Furthermore, the stability of the method is verified. Perturbations are added to the boundary conditions. Accuracy on the order of 10 −11 is obtained without noise. After adding the disturbance, the calculation accuracy is the same order of magnitude as the disturbance.

Keywords: method of fundamental solution; leave-one-out cross-validation algorithm; antiplane piezoelectricity problems; meshless method; collocation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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